Giffords will also be going to the White House on Friday, when President Obama will sign the last piece of legislation she proposed into law.
Navy Secretary Ray Mabus will host the ship-naming ceremony at the Pentagon.
Giffords is still recovering from being shot in the head in the shooting. She announced last month she was resigning from Congress, and one of her aides who was injured in the shooting is now running to take her place.
The Navy has not announced what the ship, its newest littoral combat ship (LCS), will be called. A Navy spokeswoman said she could not elaborate about whether Giffords’s and Green’s attendance was tied to the ship’s name.